Pure Mathematics is some kind of art. You cannot teach art: You may teach history of art, You may teach what works was created by some art-enabled people. So in Math is the same. If You want to educate new mathematicians You should follow with guidelines which are used in Art Academias. They are good: they accept creativity, fresh look etc. whilst still they teach about history of art, some movements, achievements of the future etc. Look: real artist is also great craftsman in his area!
In Math there is also practical aspect: applied math. Here You have to learn more crafts than art, but sometimes art goes from the air.
The only solution to problem You mentioned is to learn math in a way which is seen as interesting and important for Young people. They have ability to learn much more complicated things than calculus or even abstract algebra. If You try to play one of this newest computer games You will see that it is sometimes more difficult than proof of something maybe even non obvious. But it is different: it creates emotions. Try to create emotions learning math and You will be welcomed by them, and they will be glad to learn math! That is the way our society works: we like to entertain ourself!